Question

a constant term in the displacement function ensures??​

Answer 1

Answer:

Explanation:

1. Criteria for Convergence.

The finite element method provides a numerical solution to a

complex problem. It may, therefore, be expected that the solution must

converge to the exact solution under certain circumstances. It can be shown

that the displacement formulation of the method leads to an upper bound to

the actual stiffness of the structure. Hence the sequence of successively finer

meshes is expected to converge to the exact solution if assumed element

displacement fields satisfy certain criteria. These are,

1. The displacement field within an element must be continuous. In

other words, it does not yield a discontinuous value of function

but rather a smooth variation of function, and the variation do not

involve openings, overlap, or jumps, which are inherently

continuous. This condition can easily be satisfied by choosing

polynomials for the displacement model. The function w is

indeed continuous if for example it is expressed as,

W = C1 + C2 x + C3 x

2

+C4 x

3

+… ………… .

Answer 2

Given:

A constant term in the displacement function.

To find:

What does it signify ?

Solution:

Let us consider a displacement-time function with a constant "c" as follows:

$\therefore \: x = f(t) + c$

• Lets assume that f(t) be t^(n), where n is an integer.

$\implies \: x = {t}^{n} + c$

Now, at time t = 0 sec:

$\implies \: x_{(t = 0)} = {0}^{n} + c$

$\implies \: x_{(t = 0)} = 0 + c$

$\implies \: x_{(t = 0)} = c$

$\implies \: x_{(t = 0)} \neq 0$

So, at time t = 0 sec (i.e. when the observation on the particle began) , the position of the particle was already ahead of zero.

• Again let's consider f(t) = nt, where n is integer.

$\implies \: x = nt + c$

$\implies \: x_{(t = 0)} = n(0) + c$

$\implies \: x_{(t = 0)} = 0 + c$

$\implies \: x_{(t = 0)} = c$

$\implies \: x_{(t = 0)} \neq 0$

So, the constant ensures that the particle doesn't start from origin.